A Note on Bayesian Networks with Latent Root Variables
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909121098285056 |
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| author | Zaffalon, Marco Antonucci, Alessandro |
| author_facet | Zaffalon, Marco Antonucci, Alessandro |
| contents | We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we call empirical. A dataset of observations of the manifest variables allows us to quantify the parameters of the empirical Bayesian net. We prove that (i) the likelihood of such a dataset from the original Bayesian network is dominated by the global maximum of the likelihood from the empirical one; and that (ii) such a maximum is attained if and only if the parameters of the Bayesian network are consistent with those of the empirical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Bayesian Networks with Latent Root Variables Zaffalon, Marco Antonucci, Alessandro Machine Learning Artificial Intelligence We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we call empirical. A dataset of observations of the manifest variables allows us to quantify the parameters of the empirical Bayesian net. We prove that (i) the likelihood of such a dataset from the original Bayesian network is dominated by the global maximum of the likelihood from the empirical one; and that (ii) such a maximum is attained if and only if the parameters of the Bayesian network are consistent with those of the empirical model. |
| title | A Note on Bayesian Networks with Latent Root Variables |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2402.17087 |